Akpa Akpro, recently back in action following a broken metatarsal, kicked out at Cumbrians defender Frank Simek before the npower League One leaders slumped to a 1-0 home defeat on Saturday.
"The sending off was ridiculous really," Moore told Press Association Sport. "Akpo's just let himself down more than anything.
"He's let me down, he's let supporters down, he's let his family down and most of all he's let the lads down.
"You can't have 10 men. It doesn't matter who you're playing at this level, you can't have 10 men."
Bournemouth were the only top six side to win over the weekend, meaning Rovers retained their place at the summit on goal difference, but Moore takes little comfort from this and looks upon an opportunity missed.
"That's a disappointing thing for us, to come off the pitch and find out that only one team in the top six won," he added.
"We were expected to beat Carlisle, no disrespect to Carlisle but I think a lot of people expected it. I certainly expected it without putting it through to the players.
"We warned the players beforehand that there are no easy games at this level. Anybody can beat anybody at this level."
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